On Wednesday, New York City hit a record 59,373 people in shelters overseen by the Department of Homeless Services.

There is no clearer indicator of the homelessness crisis than in the Bronx at the intake center for families with children, where on a recent Saturday morning at 7:30, Larissa Galindo had just gotten off the bus from a temporary shelter.

“We’re tired,” Ms. Galindo, 19, said, burying her face in her hands and trying to wipe the sleep and frustration from her eyes. Unique, her 1-year-old daughter, looked up from a stroller. They had left the center, known as PATH, short for Prevention Assistance and Temporary Housing, four hours earlier.

“I want to go to sleep,” Ms. Galindo said.

In a cascade of good intentions and unintended consequences, homeless parents and their children are facing dayslong waits and sleepless nights as they flood the city’s already overwhelmed homeless services.

Under a 1999 law that was supposed to give homeless families dignity and relief, parents and children seeking shelter are not allowed to sleep at the center. Instead, those still in the process of applying for housing at 10 p.m. must be given beds for the night. The city must also transport them to and from wherever they sleep so families can continue the application process the next morning.

But with 12,913 families in homeless shelters, which is also a record, and the city trying to avoid giving them “overnights” twice in a row, New York has created a bureaucracy of sleep that, paradoxically, keeps many families from getting any rest. Some yellow school buses transporting them to shelters leave the PATH center as late as 4 a.m. People who are loaded onto them then are bused back two hours later so they can be seen by 11 a.m., before a new wave of families arrives.

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Homeless families unloading their belongings from a bus that brought them back to the Prevention Assistance and Temporary Housing intake center in the Bronx.CreditVictor J. Blue for The New York Times

As a result, overnight shelter has come to mean a few hours — or mere minutes — in a bed. Parents must haul suitcases, strollers and their children into the intake center, onto the bus, into the temporary shelter, back onto the bus and back to the PATH center.

Ms. Galindo, who works at a Fine Fare supermarket in Harlem, was lucky. After waiting hours to apply for shelter a day earlier, she got two hours of rest in a bed.

“What’s going on now is a direct result of capacity,” said Kathryn Kliff, a staff attorney at the Legal Aid Society, which is pushing the city to improve its services for homeless people. “This is not the norm. This isn’t how overnights go.”

The record number of people in shelters overseen by homeless services does not count several thousand more who are in specialized shelters for homeless youths and domestic violence victims.

The 1999 law was championed by Steven Banks, when he was a lawyer for the Legal Aid Society working to improve conditions for families with children. He is now the commissioner of the Department of Social Services overseeing homeless services.

The intent was to end the longtime practice of having families sleep overnight in chairs, on desks and on the floor of the intake office in the Bronx. The sight had become a symbol of the city’s poor management of homelessness at the time, and the city had paid $5 million in fines over four years for violating a court order to stop it.

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Because of city rules, families are not allowed to spend the night at the PATH center. To get around this rule, the city loads them onto buses and takes them to hotels or shelters, then brings them back, exhausted, a few hours later.CreditVictor J. Blue for The New York Times

“It was to end the practice of using a welfare office as a de facto shelter with families with children sleeping on the floor for days on end,” Mr. Banks said in a recent interview. “That was the intent of the law, and that’s the practice that it has eliminated. But it didn’t eliminate the lack of affordable housing. It didn’t eliminate poverty. It didn’t eliminate domestic violence.

“Those are the drivers that result, that cause people to seek shelter from us,” he said.

Wages have not kept pace with rising rents, and the city’s long-term initiatives — such as building more affordable housing, expanding rental assistance programs and increasing legal aid to tenants fighting evictions — have not kept up with the continuing surge of people who simply cannot afford to pay the rent. Mr. Banks said the number of homeless people in shelters had also risen as the city boosted efforts to shelter people living on the street, a visible sign of the crisis that the administration of Mayor Bill de Blasio has prioritized.

But August has traditionally been a month when the city sees increases, Mr. Banks and advocates for the homeless said. Families, hoping to find housing before the new school year starts, arrive at the PATH center looking for help.

The PATH center is a gleaming office building, opened in 2011 to replace an outdated one. It is across the street from an older, worn apartment building. Families said they dreaded entering, never knowing how long they might have to stay and when they might have to go back.

Inside, where parents were slumped in chairs and children were sprawled on the floor waiting hours to be interviewed by caseworkers to determine if they are eligible for more permanent shelter, tensions have run high. “It looked like a FEMA camp,” said Allen McKinney, a 29-year-old father of two, who was seeking shelter for his family after arriving from California days earlier.

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Larissa Galindo, 19, getting off a bus with other homeless families at a Department of Homeless Services intake center in the Bronx.CreditVictor J. Blue for The New York Times

Mr. McKinney, who is a gospel drummer looking for work, said he was grateful that there was somewhere to turn for help, but he and his family were weary. He and his wife, Jenee McKinney, said they arrived around 4 p.m. on Friday and got on a yellow school bus around 3 a.m. on Saturday to go to the overnight shelter. They were back at the PATH center five hours later, where they stayed until 3 a.m. on Sunday when the city placed them in a hotel in Midtown Manhattan. “I’m not complaining. We could be on the street,” said Mr. McKinney, who along with his wife asked to go by his middle name because they did not want their family to be identified as homeless.

For several months, the vacancy rate in shelters for families with children has been less than 1 percent. In a further demonstration of the whack-a-mole nature of the problem confronting the city, that unusually low rate is not only a result of the increase in homelessness among families with children, but also of the increase in the number of adult families without shelter. Adult families are any units or families without minor children.

At the adult family intake center in Manhattan, people have been sleeping overnight. While that is not against the law, the city this month has been taking steps to prevent what had become common practice there. The city had already moved 450 such families into housing that was supposed to go to families with children.

Mr. Banks said the city was opening additional shelters for adult families to relieve the pressure. “We’re moving as quickly as we can,” he said, adding that other reforms, such as expanding a program that offers potentially homeless people rental assistance, were underway.

Mr. Banks said the city was trying to get services to needy families while also carefully evaluating whether they were eligible for shelter or if they could benefit from rental assistance, intervention with a landlord or reunification with relatives who could house them.

Parents, meanwhile, are braced to wait 12 hours or more at the PATH center, where they are not allowed to bring in food. Some walk to a nearby McDonald’s or other restaurants, at the risk of missing their name when it is called. (They must eat the food outside.) Otherwise, they make do with sandwiches, graham crackers and the school-cafeteria-size cartons of milk provided by the city.

On a Sunday morning, two days after she had arrived, Ms. Galindo was back at the PATH center, waiting. The city had found her shelter in Far Rockaway, Queens, far from her job in Harlem and far from a babysitter for her 1-year-old daughter.

Unfortunately, job location is a low priority with a less than 1 percent vacancy rate, Ms. Kliff, of Legal Aid, said.

Nate Schweber contributed reporting.

A version of this article appears in print on , on Page A1 of the New York edition with the headline: Long Nights With Little Sleep for Families Seeking Shelter. Order Reprints | Today’s Paper | Subscribe